Using lexical variables or explicitly releasing references seems to fix the problem which suggests it's related to destruction order of package variables. Consider:

$perldata = bless {hello => 'world'}, 'superman';
$bar = test($perldata);
$baz = test($perldata);
my $foo = test($perldata);

$baz = undef;


sub test {
    my $o = shift;
    print "test: $o\n";
    my $m = bless {perldata => $o}, 'TQIS::test';
    return $m;
}

sub TQIS::test::DESTROY {
    my $self = shift;
    warn $self->{perldata};
}
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Prints:

superman=HASH(0x182b3dc) at noname2.pl line 18.
test: superman=HASH(0x182b3dc)
superman=HASH(0x182b3dc) at noname2.pl line 18.
Warning: something's wrong at noname2.pl line 18 during global destruc
+tion.
test: superman=HASH(0x182b3dc)
test: superman=HASH(0x182b3dc)
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Note that the "Warning: something's wrong at " text seems to get clobbered depending on things like the specific order if the ... = test lines!